The Rogoff/Reinhard v Krugman debate is more left propaganda than an actual genuine debate over economic theory or statistical measurement. There is a fascinating thread on the Econbrowser website which more than anything else demonstrates that so far as economics narrowly considered is concerned, this is not an area in which amateurs have anything to add. But as to the polemics of economic policy debate, it is an attempt, as usual, by the left to shut down and close out any discussion of views that are different from theirs. On the comments thread, I will start with the only comment that discussed the political side of this controversy:

It is rather telling to read the comments attacking Rogoff and Reinhart, and Professor Hamilton for defending them. In the Keynesian view, the notion that government spending cuts can be beneficial is so harmful that it must be fought with all necessary means. Proponents must be shown to be bad actors, hacks, liars.

If small cutbacks are beneficial, larger cuts may be proposed, and the next thing you know, the entire Keynesian edifice may be in danger. If people began to ask whether specific governmental expenditures are worth diverting funds from private use (through borrowing or taxation), then you have a problem. I think this fear is what drives the vehemence of the Keynesian crowd’s attacks on R&R and anyone who would defend them.

Now to the technical part. If R and R are wrong, who will ever know? Here is part of the defence this time from a different commenter who goes by the name Rick Stryker (which might even be his real name):

I understand the problem that many commenters aren’t familiar with technical arguments and so don’t know how to judge. Let me try to explain the weighting issue intuitively.

Let’s forget economics and look at a simple situation. Suppose we have to decide what what the legal drinking limit is going to be, i.e., the blood alcohol level before it’s unsafe to drive. We take 6 men and every day give them enough to drink to raise their blood alcohol level to some point, let’s say it’s 1 on some scale. Each day we measure each man’s reaction time. A reaction time greater than 10 is unsafe to drive. We want to know if a reading of 1 means that you are driving drunk.

We are lucky enough to do the experiment on the first man for 100 days but can only get 10 days of data each for the other 5

Here are the measured 100 reaction times of the 1st man.

8.6 8.2 10.0 7.5 9.8 7.5 10.6 8.2 7.7 8.7
9.2 9.2 8.2 10.1 10.1 7.4 9.0 10.3 8.2 9.6
8.6 9.2 9.1 9.3 9.0 7.0 9.5 9.0 7.9 9.9
9.9 8.4 9.4 9.0 7.5 8.3 9.5 8.3 6.8 10.5
8.2 9.3 7.4 8.6 10.4 9.0 10.4 8.5 10.0 8.6
8.1 8.3 9.9 8.8 9.2 9.2 10.0 8.9 6.5 8.7
8.2 9.3 9.7 6.8 8.6 7.5 8.9 12.1 8.9 9.6
9.0 10.3 10.1 7.4 9.7 7.5 9.2 7.3 8.0 9.1
8.6 8.8 7.7 8.0 8.6 10.2 8.5 9.2 9.9 8.3
9.5 11.8 8.5 9.2 7.8 6.8 8.9 10.1 8.8 9.0

You can see on many days he’s too drunk to drive but not on all or even the majority of days.

Here are the reaction times of the other 5 men.

2 3 4 5 6
1 10.4 11.5 10.1 11.3 12.5
2 9.0 11.3 8.3 12.9 13.2
3 11.4 11.6 10.0 13.2 14.0
4 11.2 12.8 9.3 11.5 12.1
5 9.5 11.1 8.7 9.9 12.8
6 11.4 10.5 8.9 13.1 12.5
7 11.4 11.7 11.4 12.6 13.1
8 11.2 12.5 10.9 11.5 13.2
9 10.8 13.2 9.2 11.5 12.5
10 12.2 12.5 10.0 11.4 13.9

Now how do we summarize our findings? If we assume that each man’s capacity to hold his liquor is the same as every other and that the only variations are in what they ate that day, etc., you would just take all 150 data points and average them. If you did that, you’d get a reaction time of 9.7. Thus, you’d conclude a blood alcohol level of 1 is OK.

However, what if you looked at the individual averages of reaction times? Here’s what you’d get for each man.

1 2 3 4 5 6
8.9 10.8 11.9 9.7 11.9 13.0

Here it becomes obvious from the individual averages that the first guy is different from everyone else–he’s much better at holding his liquor. In fact, everyone is different as we might expect but the majority are drunk on average. So, averaging the first man’s 100 data points in with the 50 of the other 5 men will exaggerate the first guy’s influence and make it look like they can all hold their liquor.

It would be better just to average the averages, in which case you’d get 11 and you’d conclude that a blood alcohol level of 1 is unsafe to drive. That summarizes what’s actually going on better.

HAP [the critics of R&R] did the first estimation and assumed that all the men were the same. R&R did the second method and assumed that the men were in fact different. You can see that the second method is more justifiable if you have any reason to believe that the men are different. Since R&R are talking about growth rates of countries, we certainly have reason to believe they are different.

Moreover, the assumption that the averages are different is the standard starting assumption when analyzing data that is both cross sectional (different men) and time dependent (different days).

Strangely enough, HAP and Krugman accused R&R of doing something non-standard and an “error” by using the second method. I hope it’s clear intuitively how this is wrong from this example. In fact, what HAP and Krugman are proposing is non-standard.

What I asked 2slugbaits [the commenter to whom this comment is addressed] to do would have established that the way we did the average over the 150 data points would have fallen out of the simpler model I gave him if he had done the math. That’s HAP. And the way we did the average of average estimates would have fallen out of the fixed effects model, if he’d done the math. That’s R&R.

Hope this helps.

I don’t know if it helped anyone else, it did help me. It didn’t help 2slugbaits who replied:

Rick Stryker You have completely wasted your time. First, what you described is not what normally passes for a fixed effects panel model. For starters, you either have to establish a separate dummy for each panel (which eats up degrees of freedom) or you have to subtract the global mean from each observation before regressing…which eliminates any time invariant variables and is one of the reasons why random effects models are preferred. You didn’t do either one, so yours is not a fixed effects model. So what you seem to think is a fixed effects model is not. Second, neither HAP nor R&R ran a fixed effects panel model. R&R just lumped things into four buckets, took a simple average of each country’s observations within each bucket, and then took an average of the country averages. That’s it. That’s all they did. HAP skipped the second step and just took an average of all observations within each bucket. That’s why I said that if you wanted to replicate what HAP and R&R and do it in an overly complicated way by treating it as a regression, then you should just regress the observations and against a constant. Which is exactly what you did:

HAP make the assumption that a(i) = a, an unknown constant, and estimate

Y(i,t) = a + e(i,t)

where “a” is a constant. But there is no need for a “t” subscript unless that is supposed to represent one of four buckets…in which case the natural choice would a “b”.

But why would anyone in his right mind do that? Why not just say “take the average”? Third, you have obviously misinterpreted what JDH was talking about when he said that R&R took a panel approach. He clearly did not mean that literally…and if he did then he should have his license revoked. JDH meant that the R&R approach captured the intuition of a fixed effects panel model in that it tried to pick-up each country’s unique features.

And really…we all know how to derive a regression using matrix algebra.

BTW, plenty of new number crunching on the R&R data came out today…and all of it crushed the core of the R&R argument. See especially Miles Kimball’s work. And he originally very sympathetic to R&R’s position but has reluctantly concluded that their work is deeply flawed and worthless.

So Rick Stryker went back again:

I’m certainly wasting my time trying to explain this to you. You are back to your semantics. What we call the models doesn’t matter. I stated precisely what the models were and asserted that estimation of one would lead to R&R and a special case of that same model would lead to HAP. I challenged you to derive the estimators and confirm or deny my claim. I could see that you didn’t seem to understand and wanted you to demonstrate some comprehension of these issues. I was very clear in what I asked you to do. You couldn’t do it. I gave you over 2 days. Now, I’ve shown you exactly how to do it and you still don’t understand. You obviously know nothing about the issues you comment about, not that that stops you or any of Krugman’s other defenders.

The point of all this was for you and others to see that when HAP and Krugman claimed that R&R did something “odd” and an “error” they were just flat out wrong. But you will not to see.

This is why I keep talking about Krugman zombies. The level of illogic and irrationality is breathtaking.

To which the following reply was returned:

This whole sorry saga of R&R is reminiscent of a similar issue with Martin Feldstein back in 1974 in which he claimed to show that Social Security reduced private savings. Like R&R, he used these results politically to push his pet cause, in his case a campaign against Social Security. Once again, years later, two other economists, after a long struggle to get the data, found a coding error in the computer program which when corrected, caused the claimed results to disappear.

Posted by: Joseph at May 30, 2013 08:57 PM

Rick Stryker I stated precisely what the models were and asserted that estimation of one would lead to R&R and a special case of that same model would lead to HAP.

So what’s your point? What I said was that the way you were approaching this is flat out stupid and convoluted. It is certainly possible to take data into something like EViews, run it through a pooled cross-sectional fixed effects model and get an answer that exactly matches the way R&R and HAP did things. But you will get exactly the same answer by taking an average of each cross-sectional unit and then taking an average of all cross-sectional units, which is how R&R actually did their analysis. Now if you want to call the former exercise a fixed effects approach, then be my guest, but it’s a mighty odd one. When people talk about fixed effects models they usually have in mind a model that has slope coefficients as well as just a constant and fixed effects deviations. No one estimates two-dimensional pooled cross-sectional data as a special case of a fixed effects model. JDH was not saying that R&R actually did anything as stupid as run the numbers through a fixed effects model. JDH’s point was that their approach tried to capture some of the intuitions of a fixed effects approach, but they did so in a more straightforward way; i.e., just simple averaging in Excel. Doing things your way makes about as much sense as wanting to go from New York to Chicago by heading east. It’s possible to do that, but not very bright. Same with your crazy example of finding a simple mean by regressing against a constant. Yes, you could also call a simple mean a special case of a linear regression, but no normal person would do that…except I will note that you in fact did just that. Go figure.

With your latest tangent I take it that you have given up trying to defend R&R’s analysis. Both of their key points have been fatally undercut. The 90% “threshold turns out to no threshold at all. And the causality issue has also collapsed. Not only do high debt/GDP ratios fail to predict lower future growth, weak exogeneity tests failed to show a causal relationship.

And as the final posting from Rick Stryker to which nothing more has been added since, we have this:

I know this is a waste of time to continue to discuss this with you, but for the benefit of whoever is not bored silly with this and wants to learn something, I’ll try again.

The question I want to answer is, “Is Krugman right that R&R used an odd estimation technique?”

In order to answer that, we need to understand what the underlying assumptions are in each estimation method. So we need to write down the conceptual models that are equivalent to the estimation techniques. I’m not saying that R&R and HAP literally ran these conceptual models using statistical software, but rather these models are equivalent to what they did. The advantage of writing the models down is that we can see the underlying assumptions clearly.

I asserted that the R&R method is equivalent to estimating the model

Y(i,t) = a(i) + e(i,t) (1)

and averaging the estimated a(i). I also asserted that the HAP method is equivalent to estimating the model

Y(i,t) = a + e(i,t) (2)

If we can agree on that, then we can immediately see that HAP is a special case of R&R in which all means are assumed to be equal. We can also see that if anyone is making an odd assumption in cross sectional data, it’s HAP not R&R. We need to resolve this question because Krugman has asserted yet again in his latest post the unsubstantiated claim that R&R used an odd estimator.

You responded to this argument with a series of points that were irrelevant. For example, the fact that R&R and HAP didn’t literally run these models is irrelevant to the argument.

To keep us on track, I narrowed the point to just the question of whether the models I wrote down are equivalent to the estimators as I asserted. I asked you to derive the estimators. That way, it’s clear whether I’m right or not. If you derive the estimators and show that they aren’t equivalent to R&R and HAP, then my argument fails. But if you derive them and get HAP and R&R, then you will have demonstrated to yourself that a key assertion in my argument is correct.

But despite my request, you did not derive the estimators. Instead, you responded again with the irrelevant point that R&R and HAP didn’t actually run these estimators. At this juncture, I realized that you really don’t understand the point at all and can’t derive these simple estimators. I was frankly annoyed that I was wasting my time with you. I was also quite irritated that you are attempting to defend Krugman when you don’t understand these issues at all.

I gave you a day before I said anything. I thought that you might try look up the solution in an econometrics book. After 2 days, I did the derivation for you.

Amazingly enough, despite the fact that I laid out the derivations for you, you are still fundamentally confused. That’s why you need a conceptual model–to avoid confusion. For example, in your penultimate comment you said

“The R&R approach is also wasteful of information because it effectively throws away the country specific variance. That’s a bad feature of any model. The HAP model at least doesn’t throw away information.”

If you look at the models I wrote down and understand the derivations, then you can see that this statement is wrong. Look at the random effects model I wrote down:

Y(i,t) = a(i) + e(i,t)

where now the a(i) are iid random variables with mean a and variance v. Now, let v, the country specific variance, go to zero, i.e., throw away the country specific variance. What do you get? Not R&R as you claimed, but HAP!!

I think the argument I have laid out is exactly what JDH was saying. It must be frustrating for him too to watch this. He can blame me for not being clear enough in explicating it but his original point on fixed vs. random effects is absolutely right.

Also, I noticed that Krugman has backed away from one of the elements of his and HAP’s smear in his latest post, and is now saying that R&R’s excluded data was not intentional and perhaps unavoidable. But he still is claiming that the R&R estimator was “odd.” I wonder if he will back away from that assertion too? He should back away from both completely but that’s not enough. He should apologize.

Who’s right on the economics and econometrics, who can say? But who won out on the political side of the debate, it is a hands down win for Krugman. But if the American economy does start to tick up, it won’t be because of some stimulus but because of the sequester which is starting to bring down the rate of growth in public spending.